Finite Group Databasebeta

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C5×#71719 #14284335

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#71719

Splittings

HallC3×C5 ⋊ #1533
SylowC3 ⋊ C5×#1533

Subgroups

subgroupG/H
centerC22×C5C2×#217
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC2×C3×C5×#124C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C4
cosocleC3×C42C23×C5
hypercenterC2×C5×#124D3
hypocenterC3C5×#1533
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C2×C5×#124

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(18,23)(22,30)(24,31)(25,32);(10,13)(11,15)(17,19)(18,22)(20,28)(21,27)(23,30)(24,32)(25,31)(26,29);(7,8)(9,10,11,14,12,13,15,16)(17,18)(19,25,27,32)(20,24)(21,23)(22,26,30,28)(29,31)

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10033);